https://neon.tech/docs/introduction/branching is exactly what the author is looking for and is the best way to do highly efficient point-in-time versioning of Postgres data I have seen so far.
I deployed NeonDB in a large enterprise client in Q2 of this year and, yes, the initial data migration is the hard part. We added 2x100gbe network cards directly on the VMware hosts where the data was so the migration to the Kubernetes cluster running NeonDB took hours instead of weeks.